Ulteriori informazioni
The A-calculus was invented by Church in the 1930s with the purpose of sup plying a logical foundation for logic and mathematics [25]. Its use by Kleene as a coding for computable functions makes it the first programming lan guage, in an abstract sense, exactly as the Thring machine can be considered the first computer machine [57]. The A-calculus has quite a simple syntax (with just three formation rules for terms) and a simple operational seman tics (with just one operation, substitution), and so it is a very basic setting for studying computation properties. The first contact between A-calculus and real programming languages was in the years 1956-1960, when McCarthy developed the LISP programming language, inspired from A-calculus, which is the first "functional" program ming language, Le., where functions are first-dass citizens [66]. But the use of A-calculus as an abstract paradigm for programming languages started later as the work of three important scientists: Strachey, Landin and B6hm.
Sommario
I. Syntax.- 1. The Parametric ?-Calculus.- 2. The Call-by-Name ?-Calculus.- 3. The Call-by-Value ?-Calculus.- 4. Further Reading.- II. Operational Semantics.- 5. Parametric Operational Semantics.- 6. Call-by-Name Operational Semantics.- 7. Call-by-Value Operational Semantics.- 8. Operational Extensionality.- 9. Further Reading.- III. Denotational Semantics.- 10. ??-Models.- 11. Call-by-Name Denotational Semantics.- 12. Call-by-Value Denotational Semantics.- 13. Filter ??-Models and Domains.- 14. Further Reading.- IV. Computational Power.- 15. Preliminaries.- 16. Representing Functions.
Info autore
Simona Ronchi Della Rocca: Full Professor of Foundations of Computer Science since 1987, Member of the Editorial Board of TOCL (ACM Transactions on Computational Logic), Member of the Organizing Committee of LICS (Logic in Computer Science), Member of the Accademy of Sciences of Torino
Luca Paolini: PhD student in Computer Science and Discrete Mathematics, Università di Genova and Université de la Mediterranée.
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Riassunto
The book contains a completely new presentation of classical results in the field of Lambda Calculus, together with new results. The text is unique in that it presents a new calculus (Parametric Lambda Calculus) which can be instantiated to obtain already known lambda-calculi. Some properties, which in the literature have been proved separately for different calculi, can be proved once for the Parametric one. The lambda calculi are presented from a Computer Science point of view, with a particular emphasis on their semantics, both operational and denotational.
